Fundamental Theorems for the Log Minimal Model Program

By O. Fujino. 2009

223 citations recorded by the source corpus.

In this paper, we prove the cone theorem and the contraction theorem for pairs (X;B), where X is a normal variety and B is an effective R-divisor on X such that KX +B is R-Cartier.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0a1b92be24ce811d807a682df8b1a7377e8ab802

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. C. Birkar
2. J. McKernan
3. Hiromu Tanaka
4. Mihai Paun
5. R. Svaldi
6. Hong R. Zong
7. O. Fujino
8. Morgan V. Brown

In Geometry and Topology

1. C. Birkar
2. O. Fujino
3. Christopher D. Hacon
4. Hiromu Tanaka
5. Mihai Paun
6. J. McKernan
7. R. Svaldi
8. Hong R. Zong

Citations in the corpus

• Existence of log canonical flips and a special LMMP (2011, result): “By the cone theorem for lc pairs proved by Ambro [2] and Fujino [14],”
• Relative adjoint transcendental classes and Albanese maps of compact Kaehler manifolds with nef Ricci curvature (2012, background): “Fujino [15] for new results and an overview of related topics from the algebraic geometry point of view.”
• Minimal model program for excellent surfaces (2016, background): “Recently, Fujino and the author established the minimal model program for Q-factorial surfaces over algebraically closed fields [6, 30].”
• Semipositivity theorems for moduli problems (2012, methodology): “For the standard notation and conventions of the log minimal model program, see [Fn11a] and [Fn17a].”
• A geometric characterization of toric varieties (2016, background): “The construction of a divisorially log terminal modification is due to Hacon and can be found in [6], [21, 3.”
• On direct images of pluricanonical bundles (2014, unknown): “, [Fujino 2011; 2014b].”
• A TRANSCENDENTAL APPROACH TO KOLL AR'S INJECTIVITY THEOREM II (2007, methodology): “rreducible component of Di1 ∩ ···∩Di l for some {i1,··· ,il} ⊂ I, where D= P i∈IDi is the irreducible decomposition. The statement of Problem 1.8 holds true when Y is a point (see, for example, [F5], [F6], [F7], and [F8]). We do not know if the statement of Problem 1.8 holds true or not under the we”
• ACC for log canonical thresholds (2012, unknown): “Follows from (2.3.4), (3.1) and (1.9) of [15].”